France Armee de l'Air Total Personnel vs DAT?

I am trying to better understand what the total number of personnel in the French 3rd Republic's Airforce (Armee de l'Air) was and whether the numbers cited by sources includes or does not include France's DAT (Defense Aerienne du Territoire) troops/units. DAT units were French interior units including static AA units (separate from Army mobile and static anti-air units), passive air observation units such as District Anti-Air Alert Centers, and searchlight units. Secondary sources I have read on the French air force seem indirectly to treat DAT as something separate from air force (and army), but they may just be making the distinction from the operational air force as opposed to the service itself.

Pierre Le Goyet states the Armee de l'Air had ~181,000 personnel in Jun 1940; and I have seen other sources state 160,000 by March 1940 and another 153,000 by May 1940.

I would estimate the DAT troops--based on Lee Sharp's French Army books--were ~80,000, so if they were part of the personnel numbers generally cited for the air force, that would leave ~100,000 for the operational air force in May/Jun1940. That may (or may not) be realistic--I haven't been able to find information on the non-flying units of the operational French air force so hard to validate. But based on what I know of (a) the HQs and flying formations in the air force (both in the flying formations directly under air force control and those assigned to Army/Corp HQs) and (b) French training units/schools (making guesses on personnel of each), if I assume ~30,000 men in airbase units (units operating/maintaining the airbase separate from flying units), ~10,000 in signals units, and ~6,000 men in the French Aerostation units (balloon observation units that were attached to the army corps), then that adds up to ~100,00 men which when combined with the ~80,000 in the DAT would add up to the total number I have seen cited, but that really is total guess work without knowing more about the non-flying units. I can also imagine there being another 80,000 men in ordnance/repair/support units (beyond the ~30,000 airbase type unit personnel already estimated) and the DAT personnel not being part of the figure cited for the air force.

Any thoughts/insights would be greatly appreciated!